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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.oct_value_ops"></a><a class="link" href="oct_value_ops.html" title="Octonion Value Operations">Octonion Value Operations</a>
</h2></div></div></div>
<h5>
<a name="math_toolkit.oct_value_ops.h0"></a>
      <span class="phrase"><a name="math_toolkit.oct_value_ops.real_and_unreal"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.real_and_unreal">Real
      and Unreal</a>
    </h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>  <span class="identifier">real</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">unreal</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
      These return <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code> and
      <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code>
      respectively.
    </p>
<h5>
<a name="math_toolkit.oct_value_ops.h1"></a>
      <span class="phrase"><a name="math_toolkit.oct_value_ops.conj"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.conj">conj</a>
    </h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
      This returns the conjugate of the octonion.
    </p>
<h5>
<a name="math_toolkit.oct_value_ops.h2"></a>
      <span class="phrase"><a name="math_toolkit.oct_value_ops.sup"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.sup">sup</a>
    </h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">sup</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
      This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()))</span></code> of the octonion.
    </p>
<h5>
<a name="math_toolkit.oct_value_ops.h3"></a>
      <span class="phrase"><a name="math_toolkit.oct_value_ops.l1"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.l1">l1</a>
    </h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">l1</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
      This return the l1 norm (<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">())</span></code>) of the octonion.
    </p>
<h5>
<a name="math_toolkit.oct_value_ops.h4"></a>
      <span class="phrase"><a name="math_toolkit.oct_value_ops.abs"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.abs">abs</a>
    </h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">abs</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
      This return the magnitude (Euclidean norm) of the octonion.
    </p>
<h5>
<a name="math_toolkit.oct_value_ops.h5"></a>
      <span class="phrase"><a name="math_toolkit.oct_value_ops.norm"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.norm">norm</a>
    </h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>  <span class="identifier">norm</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
      This return the (Cayley) norm of the octonion. The term "norm" might
      be confusing, as most people associate it with the Euclidean norm (and quadratic
      functionals). For this version of (the mathematical objects known as) octonions,
      the Euclidean norm (also known as magnitude) is the square root of the Cayley
      norm.
    </p>
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